Learned image compression aims to reduce redundancy by accurately modeling the complex signal distribution inherent in images with network parameters. However, existing practices that train models on entire dataset offline face a limitation, as the estimated distribution only approximates the general image signal distribution and fails to capture image-specific characteristics‌. To address this issue, we propose a cross-granularity online optimization strategy to mitigate information loss from two key aspects: statistical distribution gaps and local structural gaps. This strategy introduces additional fitted bitstream to push the estimated signal distribution closer to the real one at both coarse-grained and fine-grained levels. For coarse-grained optimization, we relax the common bitrate constraints during gradient descent and reduce bitrate cost via adaptive QP (Quantization Parameter) selection, preventing information collapse and narrowing the statistical distribution gaps. For fine-grained optimization, a Mask-based Selective Compensation Module is designed to sparsely encode structural characteristics at low bitrates, enhancing local distribution alignment. By jointly optimizing global and local distributions, our method achieves closer alignment to real image statistics and significantly enhances the performance. Extensive experiments validate the superiority of our method as well as the design of our module. Our project will be publicly available.